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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...by the parts. F T PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;...
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United States Calculator: Or, Arithmetic Simplified

John M'Nevin - Arithmetic - 1841 - 280 pages
...like manner 22 = 2 x 10 = 20+ 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "If a straight line be divided into any two parts...with twice the rectangle contained by the parts." Thus, let AB be divided into two parts, 6 equal to 6 squared plus 4 squared, together with twice the...
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The United States Calculator: Or, Arithmetic Simplified, in Dollars and ...

John M'Nevin - Arithmetic - 1841 - 280 pages
...like manner 22 = 2 x 10= 20 + 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "If a straight line be divided into any two parts...with twice the rectangle contained by the parts." Thus, let AB be divided into two parts, 6 and 4, the square of the whole line 10, which is 100, is...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1841 - 332 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two parts, the square of the whole line is equal to the squares of the two parts, together with tv/ice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...twice the rectangle contained by the whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the...
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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1842 - 308 pages
...and AE, and AD and EF, and AD and FB: thus expressed, AD . AB=AD . AE +AD . EF+AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole fine. Let the straight line AB be divided into any two parts in the point c ; the rectangle contained by AB, BC, together with the rectangle* AB, AC, shall be equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. F c B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB...
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Proceedings

Scotland free church, gen. assembly - 1847
...two right angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. If a straight line be divided into any two parts,...square of the whole line is equal to the squares of each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - Algebra - 1844 - 252 pages
...than in ordinary language. The proposition, (Euc. 4. 2,) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. •..-••' Let the side of a square...
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